Model for Czochralski Crystal Growth

Abstract

The Czochralski technique is the most widely applied method for the growth of large bulk single crystal. In the Czochralski crystal growth, heat and mass transfer plays an important role in the quality of grown crystal. With the performance improvement of computer, numerical simulation is becoming a more and more important measure for optimizing the conditions of crystal growth. A reasonable model is the premises for a precise numerical experiment of Czochralski crystal growth. In literature, the unbalanced surface tension along the interface of melt-gas is often ignored in the model setup typically for Czochralski crystal growth, and the melt is modeled as the incompressible flow with the Boussinesq approximation. Because of the temperature gradient in melt, the Boussinesq approximation may results in error with the strong centrifugal and Coriolis forces in melt due to crystal and crucible rotation, and a revised model of Boussinesq approximation is proposed. Our result of numerical simulation indicates that ignoring the unbalance surface tension can results in a large deviation in melt convection, especially in the three-dimensional unsteady convection, however, the revised Boussinesq model has no contribution to further improve the precision of numerical simulation under the investigated parameter conditions for 2-inch LiCaAlF₆ crystal growth.

This work was supported by the National Natural Science Foundation of China (Grant No. 10302032).